Abstract
The mammalian cochlea amplifies sounds selectively to improve frequency resolution. However, vibrations around the outer hair cells (OHCs) are amplified nonselectively. The mechanism of the selective or nonselective amplification is unknown. This study demonstrates that active force transmission through the extracellular fluid in the organ of Corti (Corti fluid) can explain how the cochlea achieves selective sound amplification despite the non-frequency-selective action of OHCs. Computational model simulations and experiments with excised cochleae from young gerbils of both sexes were exploited. OHC motility resulted in characteristic off-axis motion of the joint between the OHC and Deiters cell (ODJ). Incorporating the Corti fluid dynamics was critical to account for the ODJ motion due to OHC motility. The incorporation of pressure transmission through the Corti fluid resulted in three distinct frequency tuning patterns depending on sites in the organ of Corti. In the basilar membrane, the responses were amplified near the best-responding frequency (BF). In the ODJ region, the responses were amplified nonselectively. In the reticular lamina, the responses were amplified near the BF but suppressed in lower frequencies. The suppressive effect of OHCs was further examined by observing the changes in tuning curves due to local inhibition of OHC motility. The frequency response of the reticular lamina resembled neural tuning, such as the hypersensitivity of tuning-curve tails after hair cell damage. Our results demonstrate how active OHCs exploit the elastic frame and viscous fluid in the organ of Corti to amplify and suppress cochlear vibrations for better frequency selectivity.
Significance Statement
Active outer hair cells have been considered to selectively amplify the basilar membrane vibrations near the sound’s tonotopic location. However, recent observations from different labs showed that outer hair cells’ action is nonselective—it spreads over the broad span of traveling waves. These observations challenge the existing theory pegged to basilar-membrane mechanics. The motion at the joint between the outer hair cell and the Deiters (ODJ) cell holds the key to account for the nonselective action of outer hair cells. We show that the characteristic motions at the ODJ are explained coherently when Corti fluid acts as the medium for outer hair cell force transmission. Our results demonstrate how nonselective outer hair cell action produces selective neural responses.
Introduction
Motile outer hair cells (OHCs) modulate vibrations in the organ of Corti (OoC) to amplify incoming sounds selectively. Basilar membrane (BM) vibrations are boosted near the best-responding frequency (BF) when sounds are soft, as if active OHCs exert effort when needed. However, growing evidence shows that OHCs’ action is nonselective—OHCs exert force throughout the length of cochlear traveling waves (Cooper et al., 2018; Strimbu and Olson, 2022). Broadband OHC action inspires new suggestions on cochlear amplification that are different from classical theories based on the interactions between the BM, scalar fluids, and OHCs (Altoe et al., 2022; Guinan, 2022).
Hearing mechanics concern interactions. The interaction between the scala fluids and BM established the theoretical foundation of cochlear traveling waves (Peterson and Bogert, 1950; Lesser and Berkley, 1972; Steele and Taber, 1981). The interaction between BM and OHCs (the cochlear soundboard and its actuators) accounted for the amplification and tuning of the sensitive cochlea (Neely and Kim, 1986; Nobili and Mammano, 1996; Lim and Steele, 2002; Ramamoorthy et al., 2007). As tomographic vibrometry technology enabled researchers to observe mechanics beyond BM (into the OoC), an agenda with growing interest regards interactions between OoC substructures. Structurally prominent supporting cells or microstructures, such as the pillar cells, reticular lamina (RL), and Deiters cells, determine how OHCs interact with the BM (Nam and Fettiplace, 2010; Motallebzadeh et al., 2018; Prodanovic et al., 2019; Zhou and Nam, 2019). The geometry and mechanical properties of OoC substructures shape their vibration patterns (Zhou et al., 2022; Lin et al., 2024). Especially, vibration patterns at the OHC–Deiters cell joint (ODJ) show revealing differences between sensitive and insensitive cochlea (Cooper et al., 2018; Dewey et al., 2021; Meenderink et al., 2022). Thus, ODJ motion provides an excellent opportunity to explore the interaction between OHCs and other OoC structures. Substantial longitudinal and lateral motions of the ODJ compared with BM's transverse motion suggest that the Deiters cells bend about its root (Dewey et al., 2021; Cho and Puria, 2022; Meenderink and Dong, 2022; Frost et al., 2023).
The interaction between the OoC and the Corti fluid (extracellular fluid in the OoC) is an imperative subject because it holds the key to account for recent tomographic observations (Guinan, 2022). OoC deformation due to OHC motility must induce pressure waves along the tunnel of Corti, in addition to the pressure waves along the scala (Olson, 1999). While longitudinal coupling mediated by the scala fluids has been investigated well, another fluid coupling within the OoC began to draw attention with a growing body of new measurements relevant to the interaction. Despite the lack of empirical data, there were several exploratory studies on Corti fluid dynamics (Steele et al., 2009; van der Heijden, 2014; Ni et al., 2016; Shokrian et al., 2020; Zagadou et al., 2020). An attractive theory regarding the Corti fluid's role is that the longitudinal pressure transmission along the tunnel of Corti caused by OHC motility is a mechanism for global amplification (Karavitaki and Mountain, 2007; He et al., 2018; Zagadou et al., 2020). However, experimental evidence is either inconclusive or contradictory to the global amplification theory (Fisher et al., 2012; Dewey et al., 2019). Despite surging interests, the current understanding of the interactions between the Corti fluid and OoC structures is preliminary.
Through in vitro measurements and computer simulations, this study demonstrates how the Corti fluid mediates OHC active force. From measured data, ODJ motions in the radial plane were characterized. We exploited a computational model of the cochlea called the Virtual Cochlea that incorporates 3D OoC micromechanics, scala fluid dynamics, and the kinetics of hair cell mechanotransduction and motility. A variant of the computer model was developed to simulate our in vitro measurement conditions. After incorporating Corti fluid mechanics, our computer models could reproduce the ODJ motion characteristics observed in vitro and in vivo measurements. Interactions between the Corti fluid and OoC structures provide new insights into how the Corti fluid modulates OHC actions along the length of the traveling waves. Specifically, this study aims to illustrate how Corti fluid–OHC interaction is relevant to nonselective OHC action and to examine how the Corti fluid-mediated OHC force affects cochlear tuning and amplification.
Materials and Methods
Computational approach
Our previous computational models (Liu et al., 2017; Prodanovic et al., 2019; Zhou and Nam, 2019; Zhou et al., 2022) went through structural and fluid dynamical modifications to account for newly identified OoC motions due to OHC motility. The models consist of scala fluids (Fig. 1A,B) and 3D OoC structures (Fig. 1C,D). This study newly added Corti fluid dynamics (Fig. 1E,F). Two structural changes were required to allow large lateral (off-axis as opposed to axial) motion at the ODJ. The joints of the Corti tunnel were bracketed (Fig. 1E). The Deiters cell rootlet was represented as a pin joint, allowing lateral motion but carrying axial force. An axisymmetric fluid tube represented the Corti fluid space (Fig. 1D,E). Advanced from our previous study, which modeled only the structure-to-fluid part of Corti fluid dynamics (Shokrian et al., 2020), the Corti fluid interacts with OoC structures in this study. The Corti fluid affected OoC vibrations by applying dynamic pressures. In turn, OoC areal deformation affected Corti fluid pressure. This explicit interaction between the Corti fluid and OoC structures is central to the theme of this study—the Corti fluid as a transmission medium of OHC active forces. Material properties of the tectorial membrane and Deiters cells in the model reflected recent measurements (Zhou et al., 2022).
Computational approach. A, The fluid domain of the intact cochlear model (Virtual Cochlea). Three fluid layers are explicitly modeled: the top and bottom scala fluids (light blue) and the Corti fluid (pink). The top and bottom scala fluids interact with the upper and the lower surfaces of the OoC, respectively. The Corti fluid interacts with the OoC. The red asterisks and the arrow span correspond to the cutting sections in Figure 1A. B, Fluid domain of the in vitro cochlear model (Virtual OoC). A typical excised coil is 4 mm long (distance between the asterisks). The openings of the cochlear coil (removed interscala bones) are indicated as light blue broken lines. The FE mesh grid is finer near the structure-interacting surfaces to represent steep pressure gradients more accurately. C, An OoC section with the Corti fluid (colored in pink). The ODJ is the joint between the OHC and Deiters cell. D, Three-dimensional FE model of the OoC complex. The OHC, Deiters cell, and its process form longitudinally repeating Y-shaped structural pattern. Every structural element (line) is represented as a beam element that can elongate and bend. The lines are to indicate mechanical connectivity (i.e., their thickness and width are not illustrated realistically, unlike their length). E, A radial section of the OoC FE model. Three rows of OHCs were combined into one. The pink-colored area represents the Corti fluid. The red broken polygon illustrates a deformed OoC. Changes from our previous Virtual Cochlea (Prodanovic et al., 2019) are indicated as four brackets and a hinge (the green joints). F, Axisymmetric simplification of the Corti fluid. The Corti fluid domain was considered a circular tube with varying diameters along the cochlear length. The solid blue and broken red circles represent the undeformed and deformed radial sections. The change of the effective radius represents OoC area deformation.
Two variants of the computational model were used to translate the findings of in vitro measurements into natural cochlea conditions. They were named the Virtual Cochlea and the Virtual OoC. The Virtual Cochlea represents the intact gerbil cochlea (Fig. 1A). The Virtual OoC represents the excised cochlea in the microchamber (i.e., in vitro conditions; Fig. 1B). The two models are different in terms of mechanical and electrical boundary conditions (open scala cavities and lost endocochlear potential) and the dimensions (reduced length). For instance, the span between two asterisk symbols in the models (Fig. 1A,B) corresponds to the excised span of the gerbil cochlea.
The two models share the same governing equations and model parameters (i.e., they differ only in the length of the cochlea and the fluid boundaries). For structural mechanics, 3D finite element (FE) model was used (Nam and Fettiplace, 2010; Zhou et al., 2022) to represent the OoC anatomical features realistically, including the triangular tunnel of Corti and the Y-shaped structure formed by the OHC and the Deiters cell (Fig. 1D). There are multiple nodes over a radial section of the tectorial membrane and BM so that their bending deformations can be represented more realistically. Despite having only two nodes at their extremes, the RL, OHC, and Deiters cell still can bend because the nodes have angular displacement components. Notable simplifications include the single row of OHC–Deiters cell pair reduced from three rows (Fig. 1D) and the reduction of 3D fluid into a 2D fluid domain (Fig. 1A,B,F).
Scala fluid dynamics was modeled as a potential flow (incompressible, inviscid, and irrotational flow) of which kinematic boundary conditions are described by structural mechanics (Fig. 1A):
Unlike the scala fluid, the Corti fluid was considered viscous, reflecting smaller spatial dimensions. The Corti fluid dynamics was governed by the following:
The Corti fluid interacts with the scala tympani fluid through the permeable BM. In the structural model, the Corti fluid space was represented by the filled polygon in Figure 1E. The change of the Corti fluid cross-sectional area
Fluid dynamical responses to 10 and 2 kHz stimulations are illustrated in Figure 2. In our previous studies, the scala fluid dynamics were validated against physiological studies such as scala fluid pressure peaks and notches due to the interaction between fast and slow waves (Kale and Olson, 2015; Liu et al., 2017) and the effect of fluid viscosity on cochlear sensitivity (Wang and Olson, 2016; Prodanovic et al., 2019). The simulated results of Corti fluid velocity and pressure fields and the scala pressure field looked reasonable: The pressure varied modestly in the transverse direction within the Corti fluid space (Fig. 2C). The pressure difference across the permeable basilar membrane was smaller than that across the upper surface of the OoC. Albeit reasonable, our observations on Corti fluid pressure and velocity warrant experimental validations. To our knowledge, no measurements of Corti fluid dynamics have been reported to date, except for a measurement from excised (opened) cochlea (Karavitaki and Mountain, 2007).
Fluid dynamical responses. The Virtual Cochlea was stimulated at 10 and 2 kHz. Respective responses peak at 4 and 8 mm (left and right column panels). A, Corti fluid responses at 10 kHz. From top to bottom, longitudinal velocity, transverse velocity, and pressure fields are presented as normalized color contours (blue, velocity; red, pressure) and a snapshot of velocity profiles along the depth (blue profiles at four sections). Considering the axisymmetry, only half of the space is shown. B, Scala fluid responses at 10 kHz. The cochlear cavity is partitioned by the OoC, represented by solid and broken lines in the middle. The broken line represents the basilar membrane, a permeable wall between the scala fluid and the Corti fluid. The pressure waves propagate from the oval window toward the apex. The bottom plot is an expanded view to illustrate the pressure gradient across the Corti fluid. Note the sharp pressure change across the OoC top surface (the asterisk symbol). The pressure gradient is much smaller across the basilar membrane. C, D, Fluid dynamical responses to a 2 kHz stimulation.
The model explicitly incorporates the mechanotransduction kinetics of stereocilia and electromotility of OHCs. After assuming the coherent (nonsplaying) motion of the hair bundle, unlike ex situ hair bundles (Nam et al., 2015), hair bundle mechanics were reduced to a single degree of freedom representing the bundle tip deflection (i.e., the hair bundle was represented by a spring-hinged bar). Hair cell mechanotransduction followed the simplistic two-state model incorporating the adaptation according to the first-order kinetics (Prodanovic et al., 2019). OHC receptor potential was determined by the conductance and capacitance of the hair bundle and the cell body (Prodanovic et al., 2019). Three electrical nodes, representing the electric potentials at the scala media, OHC, and the extracellular compartment in the OoC, were also connected along the length of the cochlea (Zhou and Nam, 2019). OHC transmembrane potential change
The governing equations of structural mechanics, fluid dynamics, and electrophysiology were solved simultaneously (i.e., unknown degrees of freedom include displacements, fluid pressures, mechanotransduction conductance, and electrical voltages) in the frequency domain. The simulations and pre- and postprocessing were conducted using custom-written Matlab codes. No specific toolbox or function library was used other than a generic linear algebra library (LAPACK). The model has approximately half a million degrees of freedom. The fluid domains were discretized using quadrilateral elements. The mechanical properties of 3D OoC structures remained similar to those in the previous model (Prodanovic et al., 2019; Zhou et al., 2022). The simulations were run on a workstation with two 16-core Intel Xeon Processors. The minimum required RAM was 25 GB to solve the large model (Virtual Cochlea). It took up to 2 min to solve for one stimulating frequency. The model parameters are presented in Table 1.
Model parameters
Experimental approach
Young Mongolian gerbils (15–30 d old, both sexes) were used for experiments according to the institutional guidelines of the University Committee on Animal Resources at the University of Rochester. The cochleae were acutely isolated and placed in a dissection dish filled with artificial perilymph (in mM: 145 sodium gluconate, 7 NaCl, 3 KCl, 5 NaH2PO4, 0.1 MgCl2, 5 D-glucose, 0.1 CaCl2, 5 HEPES, pH 7.3–7.4, 300 mOsm). Measurements were made at three target locations: 4.2, 6.5, and 8.5 mm from the basal end (Fig. 3A). Leaving only a single turn centered at the target location, the apical and basal turns were removed before being placed in the microchamber. The interscala bones were removed using forceps to expose the target location (Fig. 3B, broken lines). The microchamber was designed to deliver alternating fluid pressures and electrical currents (called the “M-stim” and “E-stim,” respectively, throughout this study). Further details of our preparation procedures were described in our previous studies (Zhou et al., 2022; Lin et al., 2024).
Two-dimensional vibrations measured from an excised gerbil cochlea. A, The measurement location at 6.5 mm presented as a darker segment. The two asterisks indicate where the coil was cut to isolate a single turn (the darker span of the coil). The arrow span indicates an opening of 0.8–1 mm due to the removal of inter-scala bones. B, An illustration of the excised cochlea. The broken blue lines indicate removed inter-scala bones. The outer hair cell-Deiters cell joint (ODJ) is the region of interest of this study. C, Measured data at two orientation angles. The red-color data set was collected at two focal levels in this example. The ODJ is indicated with a rectangle, like panel B. A representing set of responses due to mechanical stimulations (M-stim, D–G) and electrical stimulations (E-stim, H–K) measured at 8.5 mm location are presented. The first and second rows represent the amplitude and phase data, respectively, on top of corresponding B-scan images. D–G, Vibrations to 0.8 kHz M-stim. The first and second columns demonstrate the transverse and radial motions, respectively. The outer pillar cell root and the RL vibrated most in the transverse and radial directions (red rectangles). H–K, Vibrations to 0.75 kHz E-stim. The ODJ vibrates (red rectangle) most by E-stim. Dataset used: M0227 of 2020 and E0826 of 2022.
A commercial optical coherence tomography (OCT) imaging system was used for vibration measurements (Ganymede, Thorlabs; center wavelength of 900 nm; A-scan rate 60 kHz; customized for 20× NA 0.4 objective). The OCT system was driven by a custom-written Matlab program. We ran 30–50 M-scans over the radial span of the OoC (Fig. 3C). In some cases, the measurements at one orientation were performed at two focal depths to acquire cleaner signals (Fig. 3C, the red-colored data at θ1). Stimulations were multitone complexes, containing 16–22 frequencies over three octaves of frequency range, two octaves below and one above the expected CF at the target locations. By analyzing vibration measurements at two orientation angles, 2D vibration patterns of the OoC radial section were reconstructed (Fig. 3D–K; for details of 2D analysis see, Zhou et al., 2022; Lin et al., 2024). Because this study was focused on the 2D motion at the ODJ (Fig. 3B,C, broken rectangles), we made sure that the anatomical points were clearly identified with sufficient data points.
Data, extended data, and codes
All the codes used to generate the results in this study, as well as all experimental data, relevant analysis codes, and extended data are available through the following depositories.
Source codes: https://github.com/ur-nam/vc-Corti-fluid
Experimental data: https://doi.org/10.6084/m9.figshare.25674612
Extended Data Figure 1-1: https://doi.org/10.6084/m9.figshare.27284556.v1
Extended Data Table 1-1: https://doi.org/10.6084/m9.figshare.27284613.v1.
Results
Four data types are presented in this study—in vitro measurements, in vivo data (from the literature), and computer model simulations from the Virtual OoC and the Virtual Cochlea. For in vitro measurements, the responses induced by electrical and mechanical stimulations, referred to as “E-stim” and “M-stim,” correspond to OoC vibrations due to OHC motility and transepithelial fluid pressures, respectively. The Virtual OoC represents an excised gerbil cochlea to explicitly simulate the E-stim and M-stim conditions. The Virtual Cochlea represents an intact gerbil cochlea to simulate sensitive and insensitive responses, referred to as “active” and “passive” results. The two models differ in their length and boundary conditions. The excised cochlear model is shorter, has wide artificial openings, and has no endocochlear potential. Besides these differences, the two models share the same governing equations and parameters.
Figure 3 presents a representing set of 2D vibration measurements (in vitro measurements). The Virtual OoC was validated by comparing its ODJ motions with in vitro measurements (Fig. 4). The rest of the results are Virtual Cochlea simulations (Figs. 5–9). In Figure 5, simulated responses are compared with in vivo data from the literature. Different aspects of ODJ motions are presented in Figures 6⇓⇓–9, such as frequency responses for three-axis components (Fig. 6), different OoC motions in the traveling wave peak and tail (Fig. 7), factors determining ODJ motion (Fig. 8), and the effect of local OHC motility inhibition on cochlear amplification (Fig. 9).
Measured and simulated motion at the ODJ. A, B, OoC motion trajectory from E-stim and M-stim measurements. The colors indicate the phase of motion. C, D, Comparison of motion trajectories obtained from measurements and Virtual OoC simulations. Motion trajectories at three anatomical points (the tip of the Corti tunnel, OHC top, and ODJ) are shown for measured (black curves) and simulated (red curves) results. The FE model used anatomical data to represent the geometry accurately (the gray lines and dots are the FE model). The direction of ODJ motion is defined as the angle between the primary axis of motion trajectory and the axis of the Deiters cell (θ). E, Comparison of ODJ motion angle at three tonotopic locations. The ODJ motion angle was obtained from experiments and model simulations at three different locations: 4.2, 6.5, and 8.5 mm. The filled makers and error bars indicate the mean and standard deviation of measured θ values from (n) samples. Dataset used: E0906, M0927, E0927, E1212, E1220 of year 2022 and E0123, M0123, M0516, M0518, E0614, E0616, M0616, E0623, M0623, E0705, E0717, M0717, M0720, E0818, M0818 of 2023.
Virtual Cochlea responses and relevant data from the literature. A, In vivo data from Narayan et al. (1998). Neural and mechanical tunings from the same tonotopic location were comparable near the BF, but not toward low frequencies. B, In vivo data from Cooper et al. (2018). The frequency responses of the BM and “hot spot” vibrations were compared. C, Virtual Cochlea responses presented similarly to Narayan et al.'s. As our model does not incorporate neural responses, the RL responses were presented instead. D, Virtual Cochlea responses presented similarly to Cooper et al.'s. We considered the ODJ to be comparable with their “hot spot.” Note that Cooper et al.'s is vibration along their optical axis, while ours is the vector sum of 3D vibrations. ∼20 kHz to 4 mm location (∼10 kHz).
Frequency response of ODJ in three directions—Virtual Cochlea simulations. A, The transverse motion at the arcuate-pectinate junction of BM. The ODJ motion in the transverse (B), radial (C), and longitudinal directions (D). The three sets of curves in each panel are the frequency responses at 4, 6, and 8 mm from the base. The solid and dashed lines represent active and passive responses, respectively. Displacement amplitudes are presented as a gain in dB with respect to the stapes. The red-/blue-colored shades indicate where active responses are greater/smaller than passive responses. The BM and ODJ transverse motions have a finite region of amplification (the red arrows), while ODJ radial and longitudinal motions are amplified over the entire frequency range.
Frequency-dependent OHC action on OoC motion—Virtual Cochlea simulations. A, Frequency responses of transverse motion at three anatomical points. Line colors were labeled in panel E. The responses were obtained from the 4 mm location. The frequency axis is in octaves w.r.t the CF of the location (10 kHz). B, Active gain (the ratio between active and passive response) of transverse motions. C, Frequency responses of radial motion at two anatomical points (little radial motion in the BM). D, Active gain of radial motions. E, Motion trajectories at three anatomical points when active. F, Passive motion trajectories.
OHC active force transmission through the Corti fluid—Virtual Cochlea simulations. Flexible Deiters cells and the Corti fluid characterize the present model. Three model types were simulated: a previous model without the two characteristics (A, B), the present model without the Corti fluid (C, D), and the present model (E, F). Top-row panels, Motion trajectories of active cochlea at the RL, ODJ, and BM. Bottom-row panels, Frequency responses of the three anatomical points. The displacement is the vector sum of 2D vibrations in the cross-sectional plane. The passive response is shown only for the BM (the broken curves).
Local inhibition of OHC motility—Virtual Cochlea simulations. OHC motility was inhibited over a 1 mm span (panel A inset, the extent of inhibition gradually varies from complete inhibition at the center to none at 0.5 mm from the center of inhibition). The vibrating patterns over the cochlear length were analyzed. A, BM's transverse motion over the cochlear length. Black solid and broken lines are active and passive responses of the control case. Colored curves represent the spatial patterns when OHCs were locally inhibited at four locations (square symbols). B, Gain change at the BF location due to the local inhibition. C, D, RL's transverse motion. E, F, ODJ radial motion. The simulated tone was 10 kHz, which peaks near 4 mm.
Two-dimensional vibrating patterns of the OoC due to M-stim and E-stim
Characteristic OoC motions driven by the scala fluid pressures (M-stim) and OHC motility (E-stim) provide insights into passive and active force transmissions in the OoC (Zhou et al., 2022; Lin et al., 2024). Figure 3 presents the vibration amplitude and phase in the transverse and radial directions due to M-stim (panels D–G) and E-stim (panels H–K) measured from an excised gerbil cochlea. The OoC vibrated in phase for M-stim except for the radial motion in the lateral part (Fig. 3E,G). In contrast, there was a steep phase change (>120°) across the OoC cross section for E-stim (Fig. 3I,K). For M-stim, the transverse OoC motion was greatest in the middle of the OoC (Fig. 3D, broken rectangle), and the radial OoC motion was greatest at the RL (Fig. 3F, broken rectangle). In contrast, for E-stim, both the transverse and radial motions are greatest in the OHC region (Fig. 3H,J). M-stim (transepithelial pressures) induced the relative radial motion between the tectorial membrane and the RL (Fig. 3F, broken rectangle), which drives inner hair cell hair bundle deflection. The most prominent difference between the M-stim and E-stim responses can be narrowed down to the ODJ motion (Fig. 3J, broken rectangle). Specifically, the large radial motion of the ODJ distinguishes the OoC motion due to OHC motility. In the following (Fig. 4), we quantify the ODJ motion.
Validating the virtual OoC and the virtual cochlea
Using the two computer models (Virtual OoC and Virtual Cochlea), we applied our findings of in vitro OoC mechanics to account for observations in the natural cochlea. Before doing so, we validated the model in two stages, focusing on the ODJ motion due to OHC motility. First, the ODJ motion trajectory of the Virtual OoC was compared with measured motion trajectories at three tonotopic locations. Second, Virtual Cochlea frequency responses at BM, RL, and ODJ were compared with relevant in vivo measurements in the literature.
The computational model could reproduce measured ODJ motions due to M-stim and E-stim. Decomposed 2D motions in Figure 3 were presented as vibrating trajectories in Figure 4A,B. The motion trajectories due to the M-stim showed that the OoC approximately rotates about the root of the inner pillar cell (Fig. 4B). The motion trajectories due to E-stim had no prominent center of rotation. Depending on the stimulus type, the ODJ motion was distinct in its vibrating directions. The ODJ motion was quantified by the angle between its vibrating axis and the Deiters cell axis (Fig. 4C, θ). Because our OoC mechanics reduced the three rows of OHC–Deiters cell pairs into a single-row pair, the sole ODJ node in our computer model is inevitably ambiguous. For comparison with simulations, we used the second-row ODJ measurements. We simulated stimulating conditions equivalent to E-stim and M-stim (alternating electric currents and transepithelial pressures). In Figure 4C,D, simulated motion trajectories (the red curves) at the pillar cell top, RL, and ODJ are shown together with the measured trajectories (the black curves). For further quantification, the motion angle of the ODJ (θ) was measured at three different locations over a 4 mm span of the gerbil cochlea. The ODJ motion angle under E-stim was >35° (Fig. 4E, black square symbols). In contrast, the angle was <20° under M-stim (Fig. 4E, black circular symbols). The angle decreased toward the apex despite stimulation types. The model simulations (Fig. 4E, red-colored symbols without error bars) reproduced the measurement trends.
The frequency responses of the Virtual Cochlea were compared with in vivo measurements from the literature (Fig. 5). Narayan et al. (1998) reported that mechanical and neural tuning curves overlap well near the CF, but the peak-to-tail response ratio was greater in neural tuning curves as compared with mechanical tuning at BM (Fig. 5A). The difference suggests a frequency-dependent transfer function between BM and inner hair cell vibrations. In contrast, the opposite pattern of the peak-to-tail ratio was observed around the OHC region. Tomographic vibration measurements revealed differential mechanics among substructures in the OoC (Lee et al., 2015, 2016; Cooper et al., 2018; He et al., 2018; Meenderink et al., 2022). For instance, the responses near ODJ were greater than BM responses over a broad frequency range, and the peak-to-tail ratio of the frequency response curve of the ODJ region was smaller than that of BM's (Fig. 5C; Cooper et al., 2018; Cho and Puria, 2022).
The Virtual Cochlea reproduced the qualitative characteristics of in vivo frequency responses. For instance, the tuning-curve sharpness near the CF was comparable between the RL and BM responses (Fig. 5B), while the peak-to-tail response ratio was greater at the RL. Note that, among the different aspects of OoC mechanics, the RL radial displacement best represents inner hair cell stimulations, considering that the shear motion between the tectorial membrane and the RL is determined mostly by the radial motion of the RL (Fig. 3F). In this vein, our simulated tuning curve of the RL, approximating the neural tuning better than BM's tuning, is reasonable. An interesting observation is that, although the ODJ is in between BM and the RL, its tuning curve showed an even smaller peak-to-tail ratio than the BM tuning curve, which is consistent with Cooper et al.'s observation (Fig. 5C,D).
Despite the resemblances, there are quantitative differences between our simulated results and the measured. Our simulated results showed a smaller peak-to-tail ratio in general, and the difference between ODJ and BM tuning curves was less prominent than Cooper et al.'s. Our model is less sharply tuned and less amplified, even after considering the difference in model species and CF locations. The contrast in the peak-to-tail ratios between ODJ and BM is less significant than the observation of Cooper et al., which is partly ascribed to the difference in measurement directions. The OCT vibrometry measures vibrations along the optical axis. Cooper et al. stated that their optical axis might contain longitudinal and radial motions as well as transverse motion. Our ODJ motion in Figure 5D is the net amplitude combining the motions along the three axes, unlike the measurement in Figure 5C, whose direction was unclear. In the following result, we analyze the ODJ motion component by component.
ODJ frequency responses vary depending on the vibrating direction
Depending on the vibrating direction, ODJ frequency responses appeared differently (Fig. 6). The active and passive responses of BM and ODJ motion were extracted from the model at three tonotopic locations (4, 6, and 8 mm from the basal end of the gerbil cochlea). BM transverse response was amplified more and tuned better at high-frequency locations (Fig. 6A). The transverse vibration at the ODJ was similar to that of BM both in active and passive responses (Fig. 6B). Interestingly, the frequency response of ODJ radial motion was different from its transverse response when active (Fig. 6C). ODJ radial vibrations were amplified across frequencies. When passive, ODJ's longitudinal motion was much smaller than BM's transverse motion. When active, ODJ longitudinal motion was comparable with BM vibrations (Fig. 6D). In summary, OHC action boosts transverse motions locally (near the BF) for both BM and the ODJ but increased ODJ nontransverse motions broadly.
Two observations in Figure 6 were not apparent, although they were implicated. First, longitudinal motion: Although we presented ODJ longitudinal motions, we are reserved in concluding the longitudinal motion because, unlike the radial motion, we have not compared simulated longitudinal motions with dedicated measurements. A dedicated study, such as Soons et al. (2015), would be required regarding the 3D geometry of the Y-shape structure formed by the OHC and the Deiters cell, its mechanical properties such as those in Zhou et al. (2022), in vitro measurements to M-stim and E-stim, and in vivo measurements such as Meenderink and Dong (2022) and Frost et al. (2023). Second, active suppression: Active OHCs suppressed transverse vibrations in the low-frequency region (Fig. 6A,B, the solid curves below the broken curves). This trend of suppression in low frequencies was more evident in the RL, which is presented further below.
OHCs suppress and boost OoC vibrations
Active OHCs modulate OoC vibrations differently depending on frequencies, sites, and vibrating directions. Figure 7 presents the frequency responses at three anatomical sites in the transverse and radial directions. The transverse response curves of the RL and ODJ were better tuned than the radial response curves—the blue (RL) and the red (ODJ) curves in Figure 7A were narrower than those in Figure 7C. OHC active force boosted the transverse motion of BM, RL, and ODJ within half an octave from the BF (Fig. 7A,B). For low frequencies (<0.5 octaves from the BF), active OHCs suppressed RL transverse responses, but the low-frequency suppression in the BM was minimal. Consequently, the RL's active response curves have a larger peak-to-tail ratio than the BM's. ODJ's radial motion was distinguished from other response curves in that they were boosted by active OHCs over the entire frequency range (Fig. 7C, the red solid curve above the red broken curve). For the presented location (4 mm from the base), the active gain (difference between the active and passive responses) of ODJ's radial motion was ∼10 dB over a wide frequency range below the BF (Fig. 7C).
A notable finding is that active OHCs suppressed or boosted vibrations depending on structure and direction. To appraise how active OHCs modulate OoC vibration components, the active gains (Fig. 7A,C, difference between the solid and broken curves) are presented in Figure 7B,D. OHCs’ action suppressed RL's transverse motion toward low frequency by >10 dB (Fig. 7B, the shaded area with downward arrows). In contrast, OHCs’ action boosted ODJ's radial motion as much as 10 dB in the low-frequency region (Fig. 7D, the shaded area with upward arrows). Boost near the BF and suppression in low frequencies accounts for the larger peak-to-tail ratio at the RL and possibly the neural response as compared with the BM's (Fig. 5A,B). Broadband boost at the ODJ accounts for the smaller peak-to-tail ratio as compared with BM's (Fig. 5C).
The vibration trajectories of the Virtual Cochlea demonstrate how our in vitro observations of M-stim and E-stim responses are preserved and translated into sensitive (active) cochlear responses. The most prominent difference between the passive and active responses was the vibrating direction of the ODJ. While passive ODJ moved along the axis of the OHC–Deiters cell complex, active ODJ motion was predominantly lateral (perpendicular) to the OHC–Deiters cell axis, consistent with in vitro measurements in Figure 4 (i.e., E-stim/M-stim compared with active/passive). The other difference was that the trajectory was nearly straight when passive but oval when active. This trend was also observed in our measurement (Fig. 4) but less prominent than in simulations. The trajectory is straight when the motion components are in phase but becomes oval when motion components differ in phase.
To conclude, the OoC mechanics characterized in our in vitro observations (Fig. 4) were preserved under the whole cochlea condition. Such characteristic ODJ motion due to OHC action bears functional consequences: active OHCs modulate frequency responses by boosting or suppressing vibrations differently between OoC substructures.
Corti fluid as the medium for active pressure transmission
The Virtual OoC and Virtual Cochlea were modified from our previous models (Zhou and Nam, 2019; Zhou et al., 2022; Prodanovic et al., 2019; Liu et al., 2017) because of two significant updates. One is structural changes in the joints between OoC substructures. The other is the addition of Corti fluid dynamics. Investigating how these two changes affect the Virtual Cochlea responses reveals the mechanism by which OHCs differently affect the frequency responses of OoC substructures.
Figure 8, A, and B, shows the OoC motion trajectory (active) and frequency responses (active and passive) of our previous model (Prodanovic et al., 2019). Although this previous model reproduced the macromechanical characteristics, such as the amplification and tuning at the BM reasonably (Fig. 8B), the OoC motion was different from recent in vivo observations and our in vitro measurements. For instance, there was no broadband OHC action (Fig. 8B, the red curve overlaps with the broken curve toward low frequencies). At the level of OoC mechanics, the primary axis of ODJ trajectory was along the direction of OHC–Deiters cell axis (θ = −10°; Fig. 8A).
It took two structural modifications to reproduce the radial ODJ motion due to OHC motility (Fig. 8C). One was the stiffer joints of the Corti tunnel triangle. The other was a flexible Deiters cell rootlet. Specifically, the Corti tunnel joints were stiffened by adding bracing elements, and the Deiters cell joint with the BM was changed from clamped to pinned joint. While the overall compliance of OoC felt by the OHC remains the same as before (Liu et al., 2017; Extended Data Fig. 1-1), these updates maintained overall OoC compliance but stiffened its upper part (the pillar cell and the RL) while softened the lower part (the Deiters cell). These structural changes increased the lateral motion of ODJ (Fig. 8C) but abolished active force transmission from the OHCs to the OoC structures other than ODJ (Fig. 8D).
Adding the interaction between the Corti fluid and the OoC structures restored active force transmission from OHCs to OoC structures (Fig. 8E,F). OHC active force acts like an area motor to expand and squeeze the Corti fluid space, resulting in pressure changes in the Corti fluid space (Fig. 2). In turn, the pressure change driven by OHC motility differentially modulates OoC vibrations so that this Corti fluid-mediated force transmission allows greater relative motions among OoC structures. Resulting frequency responses show low-frequency suppression at the RL (the low-frequency part of the cyan curve below the broken curve) and broadband amplification at the ODJ (the red curve above the fractured curve). To conclude, the two changes to account for ODJ motion observed in vitro cochlea switched the active force transmission mechanism from elastic to viscous (Corti fluid coupled) transmission.
Effect of local inhibition of OHC motility on the cochlear amplification
Using our computational model, we examined the effect of local OHC inactivation on the traveling waves along different OoC structures (Fig. 9A,B, BM; Fig. 9C,D, RL; Fig. 9E,F, ODJ). These computational experiments were carried out to explore the global versus local amplification (Fisher et al., 2012; Dewey et al., 2019; He et al., 2022a) in the updated Virtual Cochlea. The simulation was for 10 kHz, of which the BF location was 4 mm from the base. For the inactivation profile, a raised cosine function with a 1 mm span was used (Fig. 9A, inset plot). The OHC active gain was zero at the center of the inactivation span and 0.1 nM/mV away from the span (according to Iwasa and Adachi, 1997). The center of the inhibited location changed from 1 mm apical to 3 mm basal to the BF location. The left column plots show the traveling wave envelopes of active and passive responses for the control case (the black solid and broken curves for active and passive responses) and four locally inhibited active response curves (the colored curves). Different colors represent locations of inhibition, marked with square symbols. The plots in the right column panels present the change in gain versus inactivation locations. The greatest inhibition occurred when OHCs on the BF location were inhibited. When the inhibition site was >2.5 mm basal from the BF location, OHC inhibition hardly affected the responses of any OoC structure (Fig. 9B, BM, D, RL, F, ODJ).
This local inhibition study delivers three messages. First, the prediction of OHC-driven suppression: The overall responses increased when OHCs 0.5 mm basal to the BF location were inhibited (Fig. 9, cyan-colored curves and data points). This is consistent with the argument that OHCs not only increase but decrease vibrations along the traveling waves to enhance tuning quality at the expense of amplification (Jabeen et al., 2020). Second, active pressure transmission through the Corti fluid: Unlike the inhibition-affected responses at the other places, the affected region of ODJ traveling wave envelope was highly localized (Fig. 9E). This reveals the difference in OHC force transmission to different OoC structures. While the ODJ was elastically and directly affected by individual OHCs moving the point, other OoC structures were affected indirectly by the Corti fluid that transmits the OHC force. Third, local amplification, not global amplification: Despite broadband OHC action, the amplification was local. That is, although the solid curve of ODJ is ∼20 dB above the broken curve for the entire traveling wave (Fig. 10E), the inactivation in the far basal location hardly affected the peak amplification of any OoC structures (Fig. 9B,D,E).
Area motor-like motion of the OHC region—in vitro measurements. A, B, The motions of the OHC region due to M-stim and E-stim were plotted on top of corresponding B-scan images. The measured location was 6.5 mm from the base, and the stimulating frequency was 2 kHz (A) and 1 kHz (B). C, D, From the net motion trajectory (top plots), translational motion was removed, leaving only the deforming component of motion (bottom plots). Dataset used: M0928 and E0621 of 2020.
Discussion
We investigated the consequences of complex OoC mechanics, focusing on ODJ motion, using in vitro measurements and computer model simulations. The OoC mechanics model (Virtual OoC) reproduced the characteristic motions at the ODJ measured in excised cochlear preparations. By exploiting the whole cochlear model (Virtual Cochlea), we put the findings of our in vitro measurements in context. Our results show that fluid–structure interactions within the OoC can account for several observations that are seemingly uncorrelated, such as increased ODJ motion in the sensitive cochlea (Cooper et al., 2018; Cho and Puria, 2022; Meenderink et al., 2022), broadband OHC action (Lee et al., 2016; Cooper et al., 2018; He et al., 2018; Dewey et al., 2019; Fallah et al., 2019, 2021), and the difference between neural and mechanical tuning (Narayan et al., 1998) including the hypersensitivity of tuning-curve tails after hair cell damage (Liberman and Dodds, 1984; Henry et al., 2016).
After integrating findings from measurements, our cochlear model simulations provide insights into the relationship between active force transmission by the Corti fluid and OHC's broadband action. OHCs’ action affecting OoC vibrations over the entire traveling wave implicates their global function instead of local contribution. In the following, we discuss the implications of the nonselective OHC action, such as global amplification, suppressive action, and cochlear fluid circulation.
No global amplification despite longitudinal coupling by the Corti fluid
In an experiment with excised cochleae, fluid flow along the length of the tunnel of Corti was observed when OHCs were motile (Karavitaki and Mountain, 2007). This observation led to the fluid pump hypothesis for global cochlear amplification (Zagadou and Mountain, 2012; Guinan, 2022). According to the global amplification theory, the loss of OHCs, even in a far basal region from the peak, would affect the response at the peak. This can be a reasonable explanation for the broadband OHC action. Meanwhile, experimental observations were not consistent with the theory of global cochlear amplification or suppression (Fisher et al., 2012; Versteegh and van der Heijden, 2013; Dewey et al., 2019). Our results are consistent with the area motor hypothesis (fluid pump analogy).
The motion of the OHC region, obtained from our measurements, demonstrates that OHCs operate like area motors (Fig. 10). In the left panel plots, the OHC region movements over a vibrating cycle were presented on top of corresponding B-scan images. In the bottom plot of Figure 10C,D, the translational and rotational displacements (rigid-body motion) were removed from two snapshots of motion half a cycle apart to demonstrate the area deformation. By M-stim, the OHC region was displaced but deformed minimally (Fig. 10A,C). In contrast, by E-stim, the OHC region was displaced minimally but deformed substantially (Fig. 10B,D). Another notable observation of the E-stim case is that the OHC region contracted and expanded more in the lateral direction than in the direction of OHC length. It has been widely considered that OHC motility changes OHC length or the relative displacement between the RL and BM. Our measurements (Figs. 4A, 10B) and computer model simulations (Figs. 4C, 6⇑–8) show that the lateral (off-axis) motion of the ODJ better characterizes the OHCs’ action. Figure 10B demonstrates how the OoC mechanical frame transforms the OHC actuators into area motors.
Our results are not consistent with the global amplification theory (Fig. 9), although the deformation of the OHC region is reminiscent of an area motor. The global amplification theory posits that area motors lined along a longitudinal tube serve as a hydraulic actuator that transmits power over the length for amplification at the BF location. Different from the expectation, despite the broadband OHC actions, abolishing OHC actions one octave or more basal from the BF location hardly affected the peak responses (Fig. 9). Our simulated results are consistent with others’ experiments that showed little evidence for global amplification in the live cochlea (Fisher et al., 2012; Dewey et al., 2019).
Outer hair cells can suppress cochlear vibrations
Our incorporation of Corti fluid dynamics led to two simulated observations showing that active OHCs suppress cochlear vibrations. First, RL vibrations in sensitive cochlea were amplified near the BF but suppressed toward the low frequency (Figs. 7B, 8). This low-frequency side suppression was none or negligible in the BM. Second, the local inhibition of OHCs basal to the peak resulted in relaxed (increased) vibrations in the tail region (Fig. 9, cyan-colored curves). This implies that active OHCs sharpen the tuning curve by tightening (suppressing) the response basal to the peak while amplifying the peak response (Jabeen et al., 2020). This “tightening” action of` OHCs was applied to different sites across the OoC (RL, ODJ, and BM).
The suppressive action of OHCs is in line with the previous observations on neural tuning curves. For instance, the difference between neural tuning and BM mechanical tuning can be reconciled if neural tuning is approximated by RL tuning (Fig. 5A,B). Previous studies on neural tuning reported that damaged or inhibited OHC motility flattens the tuning curve by increasing the hearing threshold near the BF while decreasing the threshold in the tail of the tuning curve. Such tail region hypersensitivity after hair cell damage has been well documented for auditory nerve responses (Liberman and Dodds, 1984; Henry et al., 2016).
While our results can provide a qualitative explanation for the neural tuning curves, we must admit that existing mechanical observations lack agreement on tuning and amplification and no existing result showed a clear sign of suppression by active OHCs (Cho and Puria, 2022; He et al., 2022b; van der Heijden and Vavakou, 2022; Strimbu et al., 2024). Moreover, our FE model has only two nodes to represent the RL (one at the tip of the Corti triangle and the other at the OHC apex). Considering that the RL bends substantially due to OHC motility (Cho and Puria, 2022; Lin et al., 2024), the observations in the medial or lateral end of the RL could be different. Despite these reservations, our results suggest that OHCs modulate rather than either amplify or suppress cochlear vibrations.
Outer hair cells as the stirrer of the cochlear fluid
Despite the incongruence with the global amplification theory, we do not argue that the nonselective OHC action is an epiphenomenon. The OHC action in the tail of the cochlear traveling waves can be reserved for a role other than cochlear amplification. Biological systems exploit an array of area motors lined along a longitudinal tube as a means of mass transport, a mechanism called the peristalsis. Our previous study (Shokrian et al., 2020) showed that the Corti tunnel with the area motor of the OHCs can function as a vessel for mass transport. According to the study, the unfavorable conditions for peristalsis, such as infinitesimal vibrations of a microtube, can be overcome by the huge phase velocity of the cochlear traveling waves (more than tens of meters per second in the tail region). This theory can explain several features of the mammalian auditory organ. For instance, no auditory epithelia other than mammals’ have such an ample extracellular fluid space. Unlike other body fluids, the fluids in the inner ear labyrinth are stationary, posing a critical maintenance challenge. The sounds and OHC actions routinely generate peristalsis-like squeezing waves toward the apex. Suppose OHCs are peristaltic actuators that use the Corti fluid as a medium for pressure transmission. In that case, the wonders of the mammalian auditory organ and the puzzling broadband OHC action are explainable coherently.
Footnotes
This work was supported by National Institutes of Health R01 DC020150 and DC014685.
The authors declare no competing financial interests.
- Correspondence should be addressed to Jong-Hoon Nam at jong-hoon.nam{at}rochester.edu.